Microscopic Approach
to Scattering of Unstable Nuclei
Kosho Minomo
K. Ogata, M. KohnoA, Y. R. Sihimizu and M. Yahiro
Kyushu University, Kyushu Dental CollegeA
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Introduction
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The properties of nuclei are obtained by analysis of nuclear reaction.
□ Conventional (phenomenological) approach
Distorted wave Born approximation (DWBA), etc.
An optical potential between projectile and target is necessary as an input.
□ Features of experiments with unstable nuclei
 The beam intensity is weak.
 Unstable nuclei are fragile.
An experiment with unstable nuclei is more difficult than that with stable
nuclei so that one cannot construct an optical potential phenomenologically.
We must construct the microscopic reaction theory.
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Schroedinger equation with resummation
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 Introduction an effective interaction
Multistep of
between th nucleon in projectile and th nucleon in target
 Schrödinger equation with resummation
M. Yahiro, K. Minomo, K. Ogata, M. Kawai, Prog. Theor. Phys. No 120 Vol. 4 (2008), 767
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Nucleon-nucleus scattering
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 Schrödinger equation with resummation
(That KMT expression)
□ Folding model
The equation for the relative motion
Folding potential
: ground-state wave function of the target
We obtain the localized folding potential with the Brieva-Rook (BR) method.
F. A. Brieva and J. R. Rook, Nucl. Phys. A 291, 317 (1977).
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Structure model
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 Hartree-Fock method with finite-range Gogny force
It is applicable to obtain the ground-state wave function of all nuclei.
The properties of many stable nuclei such as the binding energy are well reproduced.
We find that this method is reliable.
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Interaction for reaction dynamics
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 Melbourne g-matrix
Two-body interaction which depends on the target density
K. Amos, P. J. Dortmans, H. V. von Geramb, S. Karataglidis and J. Raynal,
Adv. Nucl. Phys. 25, 275 (2000).
□ The framework in this study
HF method with Gogny force
Melbourne g-matrix
BR localization
Pure theoretical framework without any parameter
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p +90Zr elastic scattering
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Stable nucleus
90Zr
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6,8He+p
elastic scattering
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Unstable nucleus
6He
Unstable nucleus
8He
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Non-locality and BR localization
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In general, nucleon-nucleus potential has non-locality.
The definition of the equivalent local potential
With the BR localization, we obtain the approximate form of
.
The essence of the BR localization is the local semi-classical approximation.
Local wave number:
The BR localized potential is obtained by self-consistent calculation for
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.
The validity of BR localization
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It is necessary to test the accuracy of the BR localization.
We have to solve the Schrödinger equations
Exact:
For only elastic scatterings, one can calculate the exact form.
BR:
We tested the validity of the BR localization by comparison of the exact
calculation and BR calculation.
K. Minomo, K. Ogata, M. Kohno, Y. R. Shimizu, and M. Yahiro, J. Phys. G
(arXiv:nucl-th0911.1184)
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Exact vs BR for p +90Zr
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90Zr
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Exact vs BR for 6He+p and 8He+p
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6He
The BR method is valid
in the wide-incident energy range.
8He
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Application
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□ For deuteron induced reaction
three-body model
Optical potentials as an input
 non-local potential
complicated
 localized potential （BR method）
useful
 Continuum-Discretized Coupled-Channels method (CDCC)
It is a standard direct reaction theory to describe real and virtual breakup.
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d +58Ni elastic scattering
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Our microscopic calculation
reproduces the data.
A success of
Microscopic CDCC
 phenomenological potential
in a case of scattering
with unstable nuclei
 non-local potential
unavailable
complicated
 localized potential （BR method）
useful
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Summary
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□ Systematic description for nucleon-nucleus elastic scattering
We formulated Schrodinger equation with resummation.
 Structure model
Hartree-Fock method with finite range Gogny force
 Effective interaction for reaction dynamics
Melbourne g-matrix interaction is recommendable.
 Localization
Brieva-Rook method is useful in a wide-incident energy region.
For nucleon elastic scattering from stable and unstable nucleus,
we succeeded to reproduce the data with no free parameters.
□ Application to the other reaction
 Framework of microscopic CDCC
Deuteron elastic scattering from 58Ni is successful.
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Future work
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□ Nucleus-nucleus scattering
Double folding potential
□ Descriptions of reaction process
Microscopic CDCC
Ex.) One-nucleon removal reaction
three-body model
 Single folding potential
between valence and target
 Double folding potential
between core and target
Analysis of reactions with unstable nuclei ⇒ New insight
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